Elementary Number Theory offers a fresh and engaging exploration of one of mathematics' most timeless and beautiful fields. Designed for master's students and advanced undergraduates, it blends classical insights with modern perspectives to reveal the elegance and power of numbers-from ancient theorems to real-world applications.
Drawing on over decades of classroom experience, the author presents a carefully sequenced development of topics, beginning with divisibility and congruences, moving through quadratic reciprocity, and culminating in contemporary themes such as cryptography. The text strikes a rare balance between rigor and accessibility, ensuring that readers not only master techniques but also develop a deep appreciation for the subject's underlying ideas.
Notably, the book introduces abstract structures earlier than most standard texts, helping students build a strong conceptual framework from the outset. It also incorporates less commonly covered but highly valuable tools, such as p-adic valuations and matrix methods for continued fractions, which open doors to richer problem-solving strategies. Richly supported by classroom-tested exercises, worked examples, and intuitive explanations, Elementary Number Theory is as effective for guided learning in the classroom as it is for self- study. Whether you are preparing for advanced research or simply seeking to experience the intellectual beauty of number theory, this book offers a rewarding journey through one of mathematics' most fascinating landscapes.
Dr. Promode Kumar Saikia retired from the North Eastern Hill University, Shillong, after a remarkable academic journey that spanned more than thirty years. His path in mathematics began in Delhi, where he completed his B.Sc. and M.Sc. from the University of Delhi in 1972. Soon after, he returned to Shillong and joined the undergraduate faculty of St. Anthony's College, an experience that laid the foundation for his long commitment to undergraduate and postgraduate teaching. He earned his Ph.D. from the University of Wisconsin-Madison, USA, under the supervision of Professor Louis Solomon. His research focused on number theory and p-adic analysis, areas that continued to inspire his scholarly curiosity throughout his career. At NEHU, Dr. Saikia was known for his clarity of instruction and his thoughtful approach to guiding students through the rigor of mathematical ideas. Over the years, he has consistently emphasized the importance of problem-solving as a pathway to genuine understanding, a principle that shaped much of his teaching philosophy. Following his retirement, he continues to remain intellectually active and deeply committed to fostering an appreciation of mathematics among learners.
